Wireline and logging while drilling (LWD) tools are often used to measure physical properties of the formations through which a borehole traverses. Such logging techniques include, for example, natural gamma ray, spectral density, neutron density, inductive and galvanic resistivity, acoustic velocity, acoustic calliper, downhole pressure, and the like. Formations having recoverable hydrocarbons typically include certain well-known physical properties, for example, resistivity, porosity (density), and acoustic velocity values in a certain range. In many applications (particularly LWD applications) it is desirable to make azimuthally sensitive logging measurements, for example, to locate faults and dips that may occur in the various layers that make up the strata.
The shape of the borehole and the standoff distances between the various logging sensors and the borehole wall often influence such azimuthally sensitive logging measurements. Parameters that characterize the size and shape of a borehole are therefore of interest in many wireline and LWD applications. An instantaneous lateral displacement vector of a downhole tool within the borehole may also be of interest. Such lateral displacement vectors, in combination with tool azimuth measurements and the borehole parameters may be useful, for example, for imaging and azimuthal logging applications, such as LWD density imaging and azimuthal resistivity measurements. The above information may also be useful for interpreting and environmentally correcting azimuthally sensitive measurements such as multi-component resistivity, and directional acoustic measurements that may be used for analyzing anisotropic electrical and elastic properties of an earth formation.
Prior attempts have been documented to develop wireline and/or LWD tools and methods for estimating borehole geometry. Many such attempts make use of a plurality of acoustic standoff measurements. For example, Birchak (in Birchak et al., “Standoff and Caliper Measurements While Drilling Using a New Formation-Evaluation Tool with Three Ultrasonic Transducers”, SPE 26494, 1993) describes a method in which a tool including three ultrasonic transducers is positioned in a borehole. The borehole is assumed to be circular and a borehole radius, an eccentering distance (the distance between the circular borehole and the center of the tool), and an azimuth are determined from the ultrasonic standoff measurements. While the Birchak method has been long used in commercial drilling operations, one drawback to that method is that the borehole shape is often not circular but rather elliptical (or some other shape). Therefore in many applications the Birchak method does not adequately represent the true borehole shape.
Priest, in U.S. Pat. No. 5,737,277, in attempting to overcome such limitations, discloses a method in which a preferably centralized tool including an acoustic transducer is rotated in a borehole. The shape of the borehole is assumed to be of quadratic form; thus the standoff measurements are fitted to an algebraic elliptical model to solve for the borehole parameters. Priest also assumes that the tool does not translate (i.e., move laterally) in the borehole during data acquisition. While this may be a suitable assumption in some wireline applications in which a centralized and/or stabilized tool is utilized, it typically leads to errors in LWD applications (in which the LWD tool along with the drill string are known to often undergo significant lateral movements in the borehole as drilling progresses). As such, the Priest method is not typically suitable for LWD applications.
Varsamis et al., in U.S. Pat. No. 6,038,513 disclose a method and apparatus for determining the ellipticity of a borehole. The method uses multiple circle-based calculations involving a statistical analysis of the standoff measurements made by three acoustic sensors in the borehole. The ellipticity (the ratio between the lengths of the major and minor axes of an ellipse) is then estimated based on the mean and standard deviation of the radius and an eccentering distance. While it may be suitable in some applications to estimate the ellipticity of the borehole, the Varsamis method does not provide for a determination of the length of the major and minor axes of the ellipse or the orientation of the ellipse. Nor does the Varsamis method provide for a determination of the tool position within the elliptical borehole.
Conventional wisdom in the industry and in the prior art suggests that at least five simultaneous transducer measurements are needed to determine the borehole parameters for an ellipse (major and minor axes and orientation) and a lateral displacement of the tool in an elliptical borehole. Even more transducer measurements would be required for boreholes having a more complex shape. The above cited prior art is representative of such conventional wisdom. In each case, for LWD applications, three standoff measurements are utilized in an attempt to determine three unknowns. Birchak assumes that the borehole is circular and attempts to determine the radius of the circle, the eccentering distance, and an azimuth. Varsamis also uses circle calculations and attempts to determine the radius of the circle and a lateral displacement of the tool in the borehole. In practice Varsamis is unable to unambiguously determine the lateral displacement of the tool, but rather determines it with a 180 degree ambiguity. Priest, on the other hand, assumes that the tool does not translate in the borehole and thus determines three different unknowns, the major axis, the minor axis, and the orientation of the assumed elliptical borehole. While it is theoretically possible, to utilize a measurement tool having five (or more) standoff sensors, such a tool would be considerably more complex than a conventional tool having three (or sometimes four) standoff sensors. Such complexity would increase fabrication and maintenance costs and likely reduce the reliability of the tool in demanding downhole environments. Furthermore, deploying five or more sensors about the circumference of a downhole tool may reduce the mechanical integrity of the tool body.
It will therefore be appreciated that there exists a need for improved methods for determining the shape of a borehole. In particular there is a need for a method for determining, substantially simultaneously, the borehole parameter vector of an elliptical borehole (or a borehole having a more complex shape) and an instantaneous lateral displacement vector between a measurement tool and the borehole.